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777dan777 [17]
3 years ago
8

The graph represents two complex numbers, z1 and z2, as solid line vectors. Which points represent their complex conjugates?

Mathematics
1 answer:
REY [17]3 years ago
4 0

Point <em>A</em> represents the complex conjugate z₁ and point L represents the complex conjugate of z₂ respectively

The complex conjugate of a complex number is a complex number that having equal magnitude in the real and imaginary part as the complex number to which it is a conjugate, but the imaginary part of the complex conjugate has an opposite sign to the original complex number

Therefore, graphically, the complex conjugate is a reflection of the original complex number across the x-axis because the transformation for a reflection of the point (x, y) across the x-axis is given as follows;

Preimage (x, y) reflected across the <em>x</em> axis give the image (x, -y)

Where in a complex number, we have;

x = The real part

y = The imaginary part

The reflection of z₁ across the x-axis gives the point <em>A</em>, while the reflection of z₂ across the x-axis gives the point <em>L</em>

Therefore;

Point <em>A</em> represents the complex conjugate z₁ and point L represents the complex conjugate of z₂

Learn more about complex numbers here;

brainly.com/question/20365080

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Answer:

The null hypothesis was not rejected at 1% and 5% level of significance, but was rejected at 10% level of significance.

Step-by-step explanation:

The complaints made by the customers of a bottling company is that their bottles are not holding enough liquid.

The company wants to test the claim.

Let the mean amount of liquid that the bottles are said to hold be, <em>μ₀</em>.

The hypothesis for this test can be defined as follows:

<em>H₀</em>: The mean amount of liquid that the bottles can hold is <em>μ₀,</em> i.e. <em>μ</em> = <em>μ₀</em>.

<em>Hₐ</em>: The mean amount of liquid that the bottles can hold is less than  <em>μ₀,</em> i.e. <em>μ</em> < <em>μ₀</em>.

The <em>p</em>-value of the test is, <em>p</em> = 0.054.

Decision rule:

The null hypothesis will be rejected if the <em>p</em>-value of the test is less than the significance level. And vice-versa.

  • Assume that the significance level of the test is, <em>α</em> = 0.01.

        The <em>p</em>-value = 0.054 > <em>α</em> = 0.01.

        The null hypothesis was failed to be rejected at 1% level of

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         bottles can hold is <em>μ₀</em>.

  • Assume that the significance level of the test is, <em>α</em> = 0.05.

        The <em>p</em>-value = 0.054 > <em>α</em> = 0.05.

        The null hypothesis was failed to be rejected at 5% level of

        significance. Concluding that the mean amount of liquid that the

         bottles can hold is <em>μ₀</em>.

  • Assume that the significance level of the test is, <em>α</em> = 0.10.

        The <em>p</em>-value = 0.054 < <em>α</em> = 0.10.

        The null hypothesis will be rejected at 10% level of

        significance. Concluding that the mean amount of liquid that the

         bottles can hold is less than <em>μ₀</em>.

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